Interactive lab · Probability theory

Probability on the Titanic

An interactive lab in probability theory, built on the passenger list of RMS Titanic (1912).

Every number on this page is computed in your browser from the actual passenger list of the Titanic, with no prepared answers. The experiment behind each probability is always the same: choose one of the 1,309 passengers uniformly at random, and ask how likely the chosen passenger is to have a given property. Classical probability, complements, the addition rule, conditional probability, the definition of independent events and distributions of random variables are all applied to this single dataset, so formulas and data can be checked against each other at every step.

Passengers on the list
Survived
P(survived)
P(survived | female) vs P(survived | male)

1The data

The dataset is titanic3, maintained by the Vanderbilt University Department of Biostatistics. It lists 1,309 passengers (the crew is not included) with ticket class, sex, age, family relations, fare and port of embarkation, plus whether the person survived the sinking on 15 April 1912.

Source file: titanic3.csv · variable description · origin of the data (Department of Biostatistics, Vanderbilt University). The principal source of the passenger records is Encyclopedia Titanica.

Variables

Caveats

  • Age is missing for 263 passengers (about one in five). Events built on age therefore use only passengers with a known age, and “age unknown” is treated as its own group.
  • Fare is missing for 1 passenger; port of embarkation is missing for 2. Rows with a missing value are excluded from calculations that need that variable.
  • These are historical records, not a random sample of any larger population: every probability on this page is computed for this list, not an estimate for Edwardian ocean travel in general.

Who was on board

2Events and the addition rule

Build two events, A and B, by pressing the buttons for the conditions you want. Every count, probability and percentage below is recomputed from the passenger list the moment a button is pressed.

2.1 Event builder

Figure 2.1. The four regions of the sample space, with passenger counts.

3Random variables

3.1 Y: family size aboard

Let be the number of people from one family on board, and define a passenger as travelling alone when . This is an empirical distribution straight from the data.

Figure 3.1. Number of passengers for each family size y, for the selected filter.

3.2 Z: ticket class

The simplest non-trivial example: with probabilities equal to the class shares of the list.

4Self-check

Practice with questions generated at random from the passenger list. Type the answer as a decimal with four places; independence questions are answered with yes/no.

Score: 0 / 0

5Formula reference

Every formula used on this page, grouped as in the course syllabus. Each entry names the section where it is applied.